Question: Solve for $x$ and $y$ using elimination. ${3x+2y = 13}$ ${-4x+5y = 21}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $2$ ${-15x-10y = -65}$ $-8x+10y = 42$ Add the top and bottom equations together. $-23x = -23$ $\dfrac{-23x}{{-23}} = \dfrac{-23}{{-23}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {3x+2y = 13}\thinspace$ to find $y$ ${3}{(1)}{ + 2y = 13}$ $3+2y = 13$ $3{-3} + 2y = 13{-3}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 1}$ into $\thinspace {-4x+5y = 21}\thinspace$ and get the same answer for $y$ : ${-4}{(1)}{ + 5y = 21}$ ${y = 5}$